Revision Notes - Unit 1
Particles
INTRODUCTION
to
Elementary Particle Physics
*
Fundamental building blocks of
which all matter is composed:
Elementary Particles
* Pre-1930s it was thought there were just
four elementary particles
electron
proton
neutron
photon
1932 positron or anti-electron discovered,
followed by many other particles (muon, pion
etc)
We will discover that the electron and photon
are indeed fundamental, elementary
particles, but protons and neutrons are made
of even smaller elementary particles called
quarks
Cosmic Rays
CLASSIFICATON OF PARTICLES
An elementary particle is a point particle without structure that is not
constructed from more elementary entities
With the advent of particle accelerator
in the 1950’s many new elementary
particles were discovered.
The question arose whether perhaps
there were too
many to all be elementary.
This has led to the need
for classification of
particles.
Year of discovery of the particles…
FUNDAMENTAL INTERACTIONS AND THE
CLASSIFICATION OF PARTICLES
Fundamental interactions
1.
2.
3.
4.
gravitation
electromagnetic
strong nuclear force
weak nuclear force
Participating particles
1.
2.
3.
4.
all particles with mass
those carrying charge
Hadrons (and quarks)
Leptons (and quarks)
HADRONS
Hadrons interact through strong forces.
There are two classes, mesons and
baryons.
Mesons have zero or integral spin (0
or 1) with masses that lie between the
electron and the proton.
Baryons have half integral spin (1/2 or
3/2) and have masses that are always
greater than or equal to that of the
proton.
Hadrons are not elementary particles. As we
will see later, they are made of quarks
LEPTONS
Leptons interact through weak interactions, but not via the strong force.
All leptons have spin of 1/2. There are
six kinds of lepton: electron e-, muon
m-, and tau t -, and 3 neutrinos ne, nm, nt
Note that each distinct neutrino is associated
with one of the other leptons
Leptons were originally
named because they
were “Light-particles”, but
we now know the Tau is
twice as heavy as a
proton
Neutrinos were originally
thought to be massless,
but they probably have a
small mass
Read more in Tipler p.
1336
Matter & Antimatter
Every particle has an antiparticle partner
Here are some examples
e- - electron
p - proton
e+ - positron
p - antiproton
n - neutron
n - antineutron
n - neutrino
n
- antineutrino
Antimatter
For each particle there is
an associated
antiparticle
Anti-particles always created in
particle-anti particle pairs
s
Electron Pair Production
g -> e- + e+
s
Eg  2 x 511 keV
e-
e+
* Antiparticle has the same mass and magnitude
of spin as the particle
* Antiparticle has the opposite
charge to the particle
* The positron is stable but has a short-term
existence because our Universe has a large supply
of electrons
* The fate of a positron is annihilation
Some Fundamental Particles
Spin
Antiparticle
Rest energy MeV
Charge
g
0
0
1
g
Leptons
Neutrino
Electron
Muon
n
em-
0
0.511
105.7
0
-1
-1
1/2
1/2
1/2
n
e
m
Meson
Pion

o
140
135
+1
0
0
0
o
Baryons
Proton
neutron
p+
no
938.3
939.6
+1
0
1/2
1/2
p-
Mass less
boson
photon
-
Particle Symbol
n
The Conservation Laws
Can a conceivable reaction or decay occur?
• Conservation of Lepton number contd:
…..because the neutrino associated with an electron is different to a
neutrino associated with a muon, we assign separate Lepton
numbers Le, Lm and Lt to the particles
e.g. for e and ne, Le=+1, for their anti-particles Le=-1, and for all other
leptons and other particles Le=0
• Conservation of Strangeness
There are other conservation laws which are not
universal, e.g. strange particles have a property called
strangeness which must be conserved in a decay or
reaction
Checking Baryon Numbers
2p+ + p + n
_
_
p+ + p + p
_
a) p+ + n
b) p+ + n
Answer: a) Baryons = 1+1 on left hand side
Baryons = 2 on right hand side too!
Allowed reaction!
b) Baryons = 2 on left hand side
Baryons = -1 on right hand side
Forbidden reaction
Checking Lepton Numbers
a) µb) π+
_
e- + n e + n m
µ+ + nm + ne
Answer: a) Before decay Le = 0 and Lm = +1
After decay Le = 0 and Lm = +1
Allowed reaction!
b) Before decay Lm = 0 and Le = 0
After decay Lm = 0 and Le = 1
Forbidden reaction!
Is Strangeness Conserved?
a) π+ + n
b) π- + p
K+ +  - + 
Answer: a) Initial state has S = 0
Final state has S = +1 - 1 = 0
Allowed reaction!
b) Initial state has S = 0
Final state has S = -1
Forbidden reaction!
Conservation Laws
• Test the following decays for violation of the conservation of
electric charge, baryon number and lepton number.
• (a) n ->   -  m  m• (b) 0 - e+ + e- + g
Conservation Laws
Solution
• Method: Use the table from the formula sheet and the
conservation laws for Baryon number and Lepton number
• (a) n ->   -  m  m– Total charge on both sides = 0 : conserved
– Baryon number changes from +1 to 0: violated
– Lm = 0 on both sides : conserved
– Process not allowed
• (b) 0 - e+ + e- + g
– Total charge on both sides = 0 : conserved
– Baryon number on both sides = 0 : conserved
– Le = 0 on both sides: conserved
– Process is allowed
Three Different Types of QUARKS
There are three elementary quarks (flavors)
That make up the fundamental particles:
Up
u
Down
d
Strange s
π+
u
d
p
Baryon
Name
Up
u
Down
d
Strange s
Spin Charge
1/2
+2/3
1/2
-1/3
1/2
-1/3
Baryon Strangeness
1/3
0
1/3
0
1/3
-1
Anti-quarks maintain spin, but change sign of S and B!
Meson
u
u
d
Different types of quarks contd.
• Mesons – quark + anti-quark q q
• Baryons – three quarks q q q
• Anti-baryons – three anti-quarks
By 1967 it was realised that new kinds of quarks were
required to explain discrepancies between the model
and experiment
Charm (c)
Bottom (b) – discovered 1977
Top (t) – discovered 1995
Quark combinations
• Find the baryon number, charge & strangeness of the
following quark combinations and identify the hadron:
• (a) uud
• (b) udd
• (c) uus
• (d) dds
Quark combinations
Solution
Method: for each quark combination determine the baryon
number B, the charge q and the strangeness S; then use Table
from formula sheet to find a match.
• (a) uud
–
–
–
–
B = 1/3 + 1/3 + 1/3 = 1
q = 2/3 + 2/3 – 1/3 = 1
S=0
It is a proton
• (b) udd
–
–
–
–
B = 1/3 + 1/3 + 1/3 = 1
q = 2/3 – 1 /3 – 1/ 3 = 0
S=0
It is a neutron
• (c) uus
– Ditto, B=1, q=1, S= -1 and it is a +
• (d) dds
– Ditto, B=1, q=-1, S= -1 and it is a -
True or false?
• (a) Leptons consist of three quarks
• (b) Mesons consist of a quark and an
anti-quark
• (c) The six flavors of quark are up,
down, charmed, strange, left and right
• (d) Neutrons have no charm
(a) False: leptons are fundamental particles e.g e(b) True
(c) False: there is no left and right quark, but there are top and bottom
quarks
(d) True: neutrons are made of udd quarks
Quark confinement
• No isolated quark has ever been observed
• Believed impossible to obtain an isolated quark
• If the PE between quarks increases with separation distance,
an infinite amount of energy may be required to separate
them
• When a large amount of energy is added to a quark system,
like a nucleon, a quark-antiquark pair is created
– Original quarks remain confined in the original system
• Because quarks always confined, their mass cannot be
accurately known
Crib sheet
(or what you need to know to pass the exam)
• The zoo of particles and their properties
–
–
–
–
Leptons (e-, m-, -, ne , nm, n)
Hadrons (baryons and mesons)
Their anti-particles
The conservation laws and how to apply them (energy,
momentum, baryon number, lepton numbers, strangeness)
• Quarks and their properties
–
–
–
–
Flavors: up, down, strange, charm, top ,bottom
How to combine quarks to form baryons and mesons
Quark spin and color
The eight-fold way patterns
• Fundamental forces and field particles
• The standard model
The Photoelectric Effect
What you need to know…
• Relationship between the energy of a photon,
and the frequency of the photon
• The electronvolt
• The work function
• Photoelectric equation
What is the photoelectric effect?
• Provides evidence that electromagnetic waves (eg
light) have particle like behaviour.
• When a metallic surface is exposed to
electromagnetic radiation (light) above a certain
frequency (called the ‘threshold frequency’) the
photons from the light are absorbed and current is
produced.
• An electron in the metal can absorb the energy from
the photon, and if there is enough energy the
electron can escape the metal!
From experimentation…
• There is no emission of electrons below the
threshold frequency.
• This frequency is different for different metals.
• Above the threshold frequency, electrons are
emitted.
• The kinetic energy of the elcectons can vary.
• Their kinetic energy is given as K.E. = 1/2 mv2
Continued…
• Increasing the frequency of the radiation, increases
the maximum kinetic energy of the electrons.
• This however has no effect on the ‘photoelectric
current’ which is the rate of emission of electrons.
• If you increase the intensity of the radiation (for
example by shining more light on the metal), will have
no effect if the frequency is still below the threshold.
• If the intensity is increased, and the frequency is
above the threshold, then you will increase the photo
electric current. (more light in = more electrons out)
What this means
Frequency BELOW Frequency ABOVE
Threshold
Threshold
Increase
frequency
If frequency still below
threshold then nothing.
If frequency is above
threshold then electrons
are emitted
Increased kinetic
energy of electrons
Increase
intensity
NOTHING
Greater
photoelectric
current
Explanation of Photoelectric Effect
• Relies on the idea of a photon being a
‘quantum’ of enegy.
• What does this mean?
• Quantum is another term for packet.
• Therefore the photoelectric affect relies on
the idea that light is not made up of waves,
but that it is made up of particles called
photons, that have packets of energy.
The relationship between the energy (E) of a
photon and its frequency (f) is:
E = hf
Where h is Plank’s constant which is equal to
6.63x10-34 Js
The Electronvolt…
This is something that always scares people
when they first see it! DON’T PANIC! It is
simply a unit used to describe energy (like
Joules).
I electronvolt (eV) is the amount of energy
needed to move 1 electron across a potential
difference of 1 volt
1 eV = 1.60x10-19 J
Einstein’s Explanation of Photoelectric
Emission
• An electron needs to absorb a minimum
amount of energy to escape from a metal.
• This minimum amount is a property of a metal
and is called the ‘work function’ ()
• If the photons hitting the metal have energy
(hf) which is less than  then no electrons are
emitted.
• Electrons can be emitted just when hf = .
The Work Function cont.
• For photons with an energy larger than , the
electrons emitted from the metal have a ranges of
energies.
• The electrons with the largest (or maximum) energy
needed the minimum energy to escape.
• Increasing the intensity of the radiation increases the
number of photons emitted, but does NOT affect the
electrons kinetic energy.
Einstein’s Photoelectric Equation
• This relates the maximum kinetic energy of the
emitted electrons to the work function and the
energy of each photon:
• hf =  + Ek
• Ek = (1/2 mv2) which is the maximum kinetic
energy.
• At the threshold frequency, Ek equals zero so hf = 